Interesting , As I understand all NI numbers end with the letters A , B , C , D , or E corresponding to the working days of the week , Mon , Tues ,Wed , Thur , Fri. My NI is ends with letter C , therefore I get paid on Wednesday. But my last 2 numerical digits also fall within the range of 40~59 which also comply with what you have said.
As far as whether one gets paid out on a weekly or 4 weekly cycle is concerned , that is something that gets asked when you initially apply for the pension , ie you get to choose which ever method of payment suits you , or at least it did so when I initially reached pensionable age 7 year’s ago.